Control for powder fusion

ABSTRACT

A powder processing machine includes a work bed, a powder deposition device operable to deposit powder in the work bed, at least one energy beam device operable to emit an energy beam with a variable beam power and direct the energy beam onto the work bed with a variable beam scan rate to melt and fuse regions of the powder, and a controller operable to dynamically control at least one of the beam power or the beam scan rate to change how the powder melts and fuses. The controller is configured to determine whether an instant set of process parameters falls within a defect condition or a non-defect condition and adjust at least one of the beam power or the beam scan rate responsive to the defect condition such that the instant set of process parameters falls within the non-defect condition.

CROSS-REFERENCE TO RELATED APPLICATION

This disclosure claims benefit of U.S. Provisional Application No.62/451,346 filed Jan. 27, 2017.

BACKGROUND

Powder bed fusion processes for additive manufacturing, such as DirectMetal Laser Sintering (DMLS), can provide advanced components in asingle manufacturing process. The process typically involves iterativelydepositing powder layers and melting/fusing select regions of the layersusing an energy beam to build up a component layer-by-layer.

Control schemes for such processes have limitations. A typical controlscheme permits a user limited control over process parameters, such aspower, speed, and path of the energy beam (e.g., a laser or electronbeam). The user controls the process via preset “themes” from which theuser can select a theme for a given geometry of a component. Forinstance, a geometry that overhangs the powder bed (a “downskin”) mayhave a corresponding theme with its own presets for a single power,single speed, and path parameters for stripe width and overlap. Outsideof selecting that theme versus another theme that has different presets,there is no ability to vary these parameters once the theme begins.

BRIEF DESCRIPTION OF THE DRAWINGS

The various features and advantages of the present disclosure willbecome apparent to those skilled in the art from the following detaileddescription. The drawings that accompany the detailed description can bebriefly described as follows.

FIG. 1 illustrates an example powder processing machine.

FIGS. 2A, 2B, and 2C illustrates powder processing defects.

FIG. 3 depicts a model for melt pool.

FIG. 4 depicts a model for balling.

FIG. 5 illustrates an example process map for balling.

FIGS. 6A, 6B, and 6C depict models for unmelt porosity.

FIGS. 7A, 7B, 7C, and 7D depict models for keyholing.

FIG. 7E illustrates an example processing map for keyholing.

FIGS. 8A, 8B, and 8C illustrates example composite process maps.

FIGS. 9 and 10 depicts models for temperature contribution from priorpasses in the same stripe.

FIG. 11 depicts a model for temperature contribution from an edgeeffect.

FIG. 12 depicts a model for temperature contribution from the priorstripe.

FIG. 13 depicts a model for temperature contribution from the priorlayer.

FIG. 14 illustrates a temperature distribution at a height above thebuild plate.

FIG. 15 illustrates a defect distribution at a height above the buildplate.

FIG. 16 illustrates a defect distribution in a three-dimensional space.

FIG. 17 illustrates a micrograph of an edge section of a component.

FIG. 18 depicts a model of an edge section of a component.

FIG. 19 illustrates a temperature profile along the edge section of FIG.18.

DETAILED DESCRIPTION

In a powder bed fusion process, aside from selecting one theme versusanother theme, there is no ability to vary process parameters once thetheme begins. Moreover, if parameters such as power, speed, and path areto be adjusted during the process, there is still the matter of how tovary such parameters to enhance melting and fusion and thus improve thequality of the components built. In this regard, the present disclosuresets forth a model-based approach for implementation of a dynamiccontrol scheme that is capable of adjusting parameters during theprocess to facilitate the production of high quality parts with fewerdefects, such as key-holing, balling, and unmelt porosity defectscommonly found in powder bed manufacturing.

The approach involves, inter alia, modeling of the melt pool, predictionof aspects such as the shape of the melt pool, energy density, andporosity. For instance, one output of the model may be a dynamic processmap of energy beam power versus speed, although other modeling inputparameters could be assessed by such process maps. Through themodelling, all input parameters may be included in the analysis and inthe 2-parameter process maps. The models are used to establish regionsin the process map where defect conditions are predicted to exist. Thus,a control scheme can plot an instant point in the build on the processmap, and adjust the power or speed to be outside of the region of thedefect conditions, thereby facilitating the production of a higherquality, lower defect component.

FIG. 1 illustrates a powder processing machine 20. The machine 20 may beused in an additive manufacturing process (e.g., powder bed fusion) tofabricate components (e.g., depicted as “build parts”). Although notlimited, the components may be gas turbine engine components, such asairfoils, seals, tubes, brackets, fuel nozzles, heat shields, liners, orpanels. Additionally, the components may be fabricated from a wide rangeof materials, including but not limited to, metal alloys.

The machine 20 generally includes a work bed 22, a powder depositiondevice 24 that is operable to deposit powder (e.g., a metal powder) inthe work bed 22, an energy beam device 26 that is operable to emit anenergy beam 28 with a variable beam power and direct the energy beamonto the work bed 22 with a variable beam scan rate to melt and fuseregions of the powder, and a controller 30 that is in communication withat least the energy beam device 26. All but the controller 30 may beenclosed in an environmental chamber 32. As will be appreciated,although not shown, the machine 20 may include additional components,such as but not limited to, a vacuum pump, process gas sources, andrelated valves.

In this example, the work bed 22 includes a build plate 22 a upon whichthe powder is deposited and the component is built. The build plate maybe actuated using a piston or the like to lower the build plate 22 aduring the process. The powder deposition device 24 may include a powdersupply bed 24 a supported on a bed plate 24 b, and a recoater arm 24 b.The bed plate 24 b may be actuated using a piston or the like to raisethe bed plate 24 b during the process. The recoater arm 24 b is operableto move across the supply bed 24 a and work bed 22, to deposit layers ofpowder in the work bed 22. The operation of the work bed 22 and powderdeposition device 24 may be controlled via the controller 30.

In this example, the energy beam device 26 includes a laser 26 a, one ormore lenses 26 b, and a mirror 26 c. The mirror 26 c may be actuated (atthe command of the controller 30) to control the direction of the energybeam 28 onto the work bed 22. The laser 26 a and one or more lenses 26 bmay be modulated (at the command of the controller 30) to control thepower of the energy beam 28. For example, the energy beam 28 can beoperated with varied energy levels from no power (off) to the highestpower setting as required to maintain processing parameters within asafe zone to mitigate defect formation. Although shown with the laser 26a, it will be appreciated that the energy beam device 26 mayalternatively utilize an electron beam gun, multiple electron beam guns,or multiple lasers, and the laser or lasers may be continuous orintermittent (pulsing).

The controller 30 may include hardware (e.g., one or moremicroprocessors, memory, etc.), software, or combinations thereof thatare programmed to perform any or all of the functions described herein.The controller 30 is operable to dynamically control at least one of thebeam power (Watts) or the beam scan rate (meters per second) to changehow the powder melts and fuses in the work bed 22. The control of powerand scan rate may also extend to “resting time” of the energy beamdevice 26, at which power is equal to zero and scan rate is equal tozero. For instance, the “resting time” parameter may be used when thepowder bed is being re-coated, and time can be added to start theprocess (which may also depend on the number of parts being built in thework bed 22 because the energy beam 28 “jumps” from one part toanother). The term “dynamically control” refers to the ability of thecontroller 30 to change at least one of the power or the scan rate asthe energy beam 28 scans across the powder to melt and fuse the powderduring an additive manufacturing process. In this regard, the controller30 is configured to determine whether an instant set of processparameters (variables) falls within a defect condition or a non-defectcondition and adjust at least one of the beam power or the beam scanrate responsive to the defect condition such that the instant set ofprocess parameters falls within the non-defect condition. For instance,the list below contains an example set of process parameter variables,which will be used in the subsequently described development of themodels upon which the dynamic control is based. In some instances,example values are listed for the variables, but it is to be understoodthat the values are variable based on the composition of the metal,energy beam, bed design, etc.

-   -   P is laser power in Watts (e.g., 285 W)    -   P′ is power injected into melt pool    -   V is laser beam velocity    -   α is laser beam absorption coefficient (e.g., 0.38)    -   ΔH_(fus) is heat of melting    -   C is metal heat capacity    -   ρ is metal density    -   D_(T) is thermal diffusivity in meters squared per second (e.g.,        5*10⁻⁶ m²/s)    -   λ is metal powder heat conductivity in Watts Kelvin per meter        (e.g., 20 W/m/K)    -   T_(m) is melting temperature of metal in Kelvin (e.g., 1600 K)    -   T_(b) is boiling temperature of metal    -   T₀ is ambient temperature or instant temperature at laser beam        location in Kelvin    -   T_(BP) is temperature of the build plate surface of the work bed    -   d_(pp) is powder particle diameter in meters    -   h is powder bed thickness in meters    -   ε is powder bed local density in grams per cubic centimeter, or        alternatively as a fraction of the density of closely packed        spheres (dimensionless)    -   x, y, and h are reference coordinates representing an instant        location in the work bed 22 in the x-direction, y-direction, and        height above the build plate 22 a, respectively

In addition to or in place of powder bed local density, powder layerthickness and compaction degree may be used. For example, piston dropmay be used (e.g., piston drop may be 40 micrometers, while the actuallayer thickness becomes 80 micrometers after the initial layers becauseof material shrinkage; the piston drops 40 micrometers after the firstlayer, but spreads 60 micrometers because the first layer shrunk by50%).

The defect condition(s) correspond to one or more specific types ofdefects often found in additive manufacturing, such as (unstsable)key-holing, balling, and unmelt porosity. Key-holing, balling, andunmelt porosity defects are depicted, respectively, in FIGS. 2A, 2B, and2C. In general, key-holing results from excessive evaporation of themelt due to high energy beam power, slow energy beam scan rate, or both;balling results from unstable elongated melt pools that break intodiscrete balls or islands; and unmelt porosity results from pockets ofunmelted powder due to low energy beam power, fast scan rate, or both.

Each of these types of defects was modeled, as discussed further below,based on the process parameter variables. The modeling, in turn, enabledeach type of defect to be mapped on a plot of energy beam power versusscan rate. Thus, for a given set of process parameter variables, theremay be one or more regions on the plot where defect conditions arepredicted to occur. In turn, if the power and scan rate at an instantlocation in the work bed 22 during a process lies within a region of adefect condition, the power, scan rate, or both, can be dynamicallyadjusted during the process such that the plot of the adjusted power andscan rate fall outside of the region of the defect condition (in aregion where non-defect conditions exist). In this manner, as the energybeam 28 scans a path across the powder to melt and fuse the powder, thecontroller 30 may dynamically adjust power, scan rate, or bothlocation-by-location along the path (e.g., voxel-by-voxel) to ensurethat at each location the power and scan rate correspond to a plotlocation on the map with a non-defect condition.

The methodology herein may also provide a technique for rapid componentqualification, wherein the output of additive manufacturing machinesensors compared with target parameters will help assess quality leveland conformance of the built components. Further, the methodology hereinmay be used to simulate a build path for entire components and then usethe simulated path to build the actual component. The control systemcould, for example, be of two types: i) follow explicitly the parametersets pre-defined for all specific locations, but monitor the parameterseparately as well to enable comparison and validation that the processwas run to plan or ii) run the controller from the start with apre-defined path, but the parameters for time, speed and power aredetermined in-process based on sensor readings and the establishedmodels. In addition to power and scan rate, the path of the energy beamcould also be adjusted either before building via the modelling (e.g.,to a less complex scan path with power and speed being the drivingfactors), or the path could be adjusted during a build (e.g., if themelt pool width varied outside its bounds, the scan spacing may beadjusted).

The following examples illustrate the mathematical modeling of defectsfor use in a dynamic control scheme.

Example 1: Modeling of Melt Pool

Referring to FIG. 3, a model of the cross-sectional area of the meltpool generated during melting of the powder was developed. Thecross-sectional area is calculated from an energy balance.ΔH _(fus)=1.47·10⁹ J/m³  Enthalpy of meltingΔH _(heat) =ρC(T _(m) −T ₀)=4.6·10⁹ J/m³  Enthalpy of heatingΔH _(fus) <<ΔH _(heat)

${{Energy}\mspace{14mu}{density}\mspace{14mu} E} = {\frac{P^{\prime}}{V} = {{1.1 \cdot 10^{2}}\mspace{14mu} J\text{/}m}}$ΔH=ΔH _(fus) +ΔH _(heat)=6.1·10⁹ J/m³  Enthalpy of heating+melting

Energy loss due to metal heating adjacent to the pool

Power  injected  into  melt  pool  P^(′) = ξα P$\xi = \left\lbrack {\sqrt{1 + \frac{A^{2}}{4}} - \frac{A}{2}} \right\rbrack^{2}$$A = {\frac{\lambda}{\alpha\; P}\left( {T_{m} - T_{0}} \right)\sqrt{2\pi\frac{\alpha\; P}{V\;\Delta\; H}}}$${{Melt}\mspace{14mu}{pool}\mspace{14mu}{cross}\text{-}{section}\mspace{14mu} S_{p}} = {\frac{\xi\; E}{\Delta\; H} = \frac{{\alpha\xi}\; P}{V\;\Delta\; H}}$

Example 2: Model of Balling

Referring to FIG. 4, balling is calculated from a modified Rayleighcondition of instability for the melt pool aspect ratio.

${{Modified}\mspace{14mu}{Rayleigh}\mspace{14mu}{condition}\mspace{14mu}\frac{l_{p}}{d_{p}}} > {\pi\;{f(\Phi)}}$

-   -   f(Φ) is a function of angle Φ (takes into account pool        stabilization by substrate)

${f(\Phi)} = \sqrt{\frac{{2{\Phi\left( {2 + {\cos\left( {2\Phi} \right)}} \right)}} - {3{\sin\left( {2\Phi} \right)}}}{{2{\Phi\left( {1 + {\cos\left( {2\Phi} \right)}} \right)}} - {2{\sin\left( {2\Phi} \right)}}}}$${{Melt}\mspace{14mu}{pool}\mspace{14mu}{diameter}\mspace{14mu} d_{p}} = {\sqrt{\frac{4S_{p}}{\pi}} = \sqrt{\frac{4}{\pi}\frac{P^{\prime}}{V\;\Delta\; H}}}$${{Solidification}\mspace{14mu}{time}\mspace{14mu} t} = \frac{l_{p}}{V}$$\left. \begin{matrix}{{Heat}\mspace{14mu}{flux}\mspace{14mu}{from}\mspace{14mu}{pool}} \\{Q = \frac{\pi\; l_{p}{\lambda\left( {T_{m} - T_{0}} \right)}}{\ln\left( {2l_{p}\text{/}d_{p}} \right)}} \\{{Energy}\mspace{14mu}{balance}} \\{{Qt} = {S_{p}l_{p}\Delta\; H_{fus}}}\end{matrix}\rightarrow\begin{matrix}{{Melt}\mspace{14mu}{pool}\mspace{14mu}{length}} \\{l_{p} = {\frac{P^{\prime}}{{\pi\lambda}\left( {T_{m} - T_{0}} \right)}\frac{\Delta\; H_{fus}}{\Delta\; H}{\ln\left( \frac{l_{p}}{r_{p}} \right)}}} \\\; \\{{\ln\left( \frac{2l_{p}}{r_{p}} \right)} \sim 2}\end{matrix} \right.$${{Balling}\mspace{14mu}{condition}\mspace{14mu}\frac{\Delta\; H_{fus}}{{\lambda\pi}\;{f(\Phi)}\left( {T_{m} - T_{0}} \right)}\sqrt{\frac{P^{\prime}V}{{\pi\Delta}\; H}}} > 1$

-   -   f(Φ) is a function of angle Φ (takes into account pool        stabilization by substrate)

Final  balling  condition${P(V)} = {{{BV}\left( {1 + {2\frac{d_{pp}}{w}} + \sqrt{1 + {4\frac{d_{pp}}{w}} - \frac{2A}{{BV}^{2}}}} \right)} - \frac{A}{V}}$$P = \frac{P^{\prime}}{\xi\alpha}$$A = {\pi^{3}\Delta\;{H\left( \frac{\lambda\left( {T_{m} - T_{0}} \right)}{\Delta\; H_{fus}} \right)}^{2}}$$w = {\frac{4\left( {1 - ɛ} \right)}{\pi}h}$$B = \frac{\pi\; w^{2}\Delta\; H}{2}$ Δ H = Δ H_(fus) + C(T_(m) − T₀)$P_{\min} = {{V \cdot \frac{1}{4}}{B\left( {1 + {4\frac{d_{pp}}{w}} + \sqrt{1 + {8\frac{d_{pp}}{w}}}} \right)}}$

FIG. 5 illustrates an example of a map of the balling condition region(shaded) on a plot of power versus scan rate.

Example 3: Model of Unmelt Porosity

FIG. 6A depicts unmelt porosity without balling, and FIGS. 6B and 6Cillustrate the assumed melt pool geometry. The model of unmelt porosityis based on a regular array of pores predicted at deterministic unmeltconditions.

${{Melt}\mspace{14mu}{pool}\mspace{14mu}{cross}\text{-}{section}\mspace{14mu}\frac{P^{\prime}}{V\;\Delta\; H}} = {\frac{2}{\pi}{w\left( {h_{0} + h_{1}} \right)}}$${{Unmelt}\mspace{14mu}{criterion}\mspace{14mu}\left( {h_{0} + h_{1}} \right)\sin\frac{\pi\; x^{\prime}}{w}} = {{\gamma\; hw} = {l_{tr} + {2x^{\prime}}}}$${{Approximate}\mspace{14mu}{equation}\mspace{14mu}{for}\mspace{14mu} w\text{:}\mspace{14mu}\left( {w + {\frac{\pi}{2}\gamma\; h} - d_{l}} \right)\left( {1 - \frac{l_{tr}^{2}}{w^{2}}} \right)} \approx {\gamma\; h}$Additional  assumption:  w = d_(l) + h₁ Unmelt  criterion:${{Without}\mspace{14mu}{balling}\mspace{14mu}\left( \frac{P^{\prime}}{V\;\Delta\; H} \right)} < {\frac{2}{\pi}{w\left( {w + {\frac{\pi}{2}\gamma\; h} - d_{l}} \right)}}$$P = \frac{P^{\prime}}{\xi\alpha}$${{With}\mspace{14mu}{balling}\mspace{14mu}\left( \frac{P^{\prime}}{V\;\Delta\; H} \right)} < {\frac{2}{\pi}{w\left( {w + {\frac{\pi}{2}\left( {\gamma + 1} \right)\gamma\; h} - d_{l}} \right)}}$

Example 4: Model of Key-Holing Porosity

Referring to FIGS. 7A, 7B, and 7C, the model of key-hole porosity isbased on a force and heat balance in a Marangoni vortex to determineflow velocity and maximal temperature under the energy beam.

${{Marangoni}\mspace{14mu}{surface}\mspace{14mu}{stress}\text{:}\mspace{14mu}\sigma_{M}} = {{\frac{\partial\sigma}{\partial T}{\nabla\; T}} \approx {\frac{\partial\sigma}{\partial T}\frac{T_{\max} - T_{m}}{l_{x}}}}$${{Marangoni}\mspace{14mu}{stress}\mspace{14mu}{is}\mspace{14mu}{equal}\mspace{14mu}{to}\mspace{14mu}{shear}\mspace{14mu}{stress}\mspace{14mu}{caused}\mspace{14mu}{by}\mspace{14mu}{viscosity}\mspace{14mu}\frac{\partial\sigma}{\partial T}\frac{T_{\max} - T_{m}}{l_{x}}} = {\eta\frac{V_{f}}{l_{\eta}}}$     l_(η)  is  laminar  sublayer  thickness$\mspace{76mu}{{{Mass}\mspace{14mu}{balance}\mspace{14mu}{for}\mspace{14mu}{green}\mspace{14mu}{zone}\mspace{14mu}\left( {{``Z"}\mspace{14mu}{in}\mspace{14mu}{{FIG}.\mspace{14mu} 7}} \right)\mspace{14mu} l_{\eta}V_{f}} = {l_{z}V}}$$\mspace{76mu}{{{Energy}\mspace{14mu}{balance}\mspace{14mu}{for}\mspace{14mu}{vortex}\mspace{14mu}\alpha\; P} = {2\lambda\frac{T_{\max} - T_{m}}{l_{T}}\frac{\pi}{4}d_{l}^{2}}}$$\mspace{76mu}{{{Heat}\mspace{14mu}{penetration}\mspace{14mu}{depth}\mspace{14mu}{into}\mspace{14mu}{vortex}\mspace{14mu} l_{T}} = \sqrt{\frac{D_{T}d_{l}}{V_{f}}}}$$\mspace{76mu}{{{thermal}\mspace{14mu}{diffusivity}\mspace{14mu} D_{T}} = \frac{\lambda}{\rho\; C}}$${{Keyhole}\text{/}{porosity}\mspace{14mu}{formation}\mspace{14mu}{criterion}\text{:}\mspace{14mu} V_{f}} = \sqrt{\frac{\partial\sigma}{\partial T}\frac{T_{\max} - T_{m}}{\eta}V}$     Typical  value  V_(f) ∼ 15  m/s${{{Keyhole}\mspace{14mu}{forms}\mspace{14mu}{when}\mspace{14mu}{recoil}\mspace{14mu}{vapor}\mspace{14mu}{pressure}} \sim {{capillary}\mspace{14mu}{pressure}\mspace{14mu}{of}\mspace{14mu}{the}\mspace{14mu}{pool}\mspace{14mu} P_{cap}}} = {\frac{\sigma}{d_{l}} = {1\;{atm}}}$$\mspace{76mu}{{\underset{\_}{{Keyhole}\mspace{14mu}{formation}\mspace{14mu}{criterion}}\text{:}\mspace{14mu} T_{\max}} = T_{b}}$$\mspace{76mu}{\frac{\alpha\; P}{2\left( {T_{b} - T_{m}} \right)\sqrt{d_{l}^{3}{\lambda\rho}\; C\sqrt{\frac{\partial\sigma}{\partial T}\frac{\left( {T_{b} - T_{m}} \right)}{\eta}V}}} < 1}$

As depicted in FIG. 7C, Marangoni flow accelerates effectivethermo-conductivity by approximately 75× and dramatically shiftscriterion of keyhole formation.

Referring also to FIG. 7D, a keyhole instability criterion is alsomodeled.

${{Keyhole}\mspace{14mu}{instability}\mspace{14mu}{criterion}^{*}\text{:}\frac{{\alpha\xi}\; P}{V\;\Delta\; H}\frac{1}{\beta\; d_{l}^{2}}} > 1$

*The numerical multiplier β=2 is determined from analysis of literaturedata

FIG. 7E illustrates an example of a map of the keyhole condition region(shaded) on a plot of power versus scan rate. In this example, there isa region where no keyhole occurs, a region where a stable keyhole occurs(which may be tolerable or acceptable), and a region where an unstablekeyhole occurs (defect region).

Example 5: Composite Process Map

FIG. 8A shows a schematic representation of a process map for an instantlocation in the work bed 22 during a process. The process map is acomposite of process maps for balling, unmelt porosity, and key-holing.That is, there is an “ideal” region on the map for which combinations ofpower and scan rate, at that location for a given starting temperatureat that location and set of process parameters, do not result inballing, unmelt porosity, or key-holing (i.e., non-defect conditions).Thus, if the power and scan rate at that location for the given startingtemperature at that location lie outside of the “ideal” region, thecontroller 30 adjusts the power, the scan rate, or both such that theadjusted power and scan rate fall within the “ideal” region fornon-defect conditions.

FIG. 8B illustrates a more detailed example of such a process map andlisting of process parameters upon which the process map is based. Asshown, there is a region where balling and unmelt porosity will occur, aregion where unmelt porosity will occur, a region where unstable keyholeporosity will occur, and a defect free region where no defects occur.For the given set of process parameters, if the power and scan rate at alocation for the given starting temperature at that location lie outsideof the defect free region, the controller 30 adjusts the power, the scanrate, or both such that the adjusted power and scan rate fall within thedefect free region (non-defect conditions). Similarly, FIG. 8Cillustrates another example process map in which at least some of thedefect regions are further classified according to a predicted defectconcentration.

Example 6: Model of Temperature at an Energy Beam Location

The instant or starting temperature at an energy beam location in thework bed 22 is modeled and may serve as the basis of the modelingexamples above. For example, the instant temperature is determined basedon at least one of the temperature of the build plate surface 22 a inthe work bed 22, the temperature change due to previous energy beampasses in a current stripe, the temperature change due to a previousstripe in the same layer, the temperature change due to previous powderlayers, or an edge factor that represents the instant location of theenergy beam in the work bed 22 relative to an edge of the componentbeing formed from the powder (collectively, “temperature factors”). Asrepresented by the equation below, the instant temperature may bedetermined based on all of these temperature factors, although it willbe appreciated that the temperature factors may be used individually orin combinations or two or more factors.

Calculation of the temperature at energy beam location, T₀:T ₀ =T _(BP) +ΔT ₁ f+ΔT ₂ +ΔT ₃

T_(BP) is temperature of the build plate surface

ΔT₁ is temperature rise caused by previous passes in current stripe

ΔT₂ is temperature rise caused by previous stripes of current layer

ΔT₃ is temperature rise caused by previous layers

f is the factor that takes into account the edge effect

With reference to FIG. 9, the stripe is the path in the y-direction. Theenergy beam passes back and forth in the x-direction along the stripe.At each pass, the energy beam is adjacent the prior pass, which addsheat to locations along the current pass. As shown in FIG. 10, thiscauses a large temperature increase immediately after the energy beamturns into a new pass because the adjacent prior pass has not had timeto cool. As the energy beam continues in the x-direction though, theimmediately adjacent pass has had more time to cool and thus adds lessheat.

     Δ T₁  (previous  passes  in  current  stripe):${\Delta\;{T_{1}(x)}} = {{T_{1x}(x)} - T_{1} - {\frac{\alpha\; P}{2{\pi\kappa}\sqrt{L^{2} + l_{tr}^{2}}}{\log\left( {1 - {\exp\left( {- \frac{V\left( {\sqrt{L^{2} + l_{tr}^{2}} - L} \right)}{2D_{T}}} \right)}} \right)}}}$$\mspace{76mu}{{T_{1x}(x)} = {\frac{\alpha\; P}{2{\pi\kappa}\sqrt{{4x^{2}} + l_{tr}^{2}}}{\exp\left( {- \frac{V\left( {\sqrt{{4x^{2}} + l_{tr}^{2}} - {2x}} \right)}{2D_{T}}} \right)}}}$$\mspace{76mu}{T_{1} = {\frac{\alpha\; P}{2{\pi\kappa}}\frac{1}{\sqrt{L^{2} + l_{tr}^{2}}}{\exp\left( {- \frac{V\left( {\sqrt{L^{2} + l_{tr}^{2}} - L} \right)}{2D_{T}}} \right)}}}$

P is laser power

α is laser absorptivity

V is scanning velocity

L is stripe width

l_(st) is hatching distance

κ is thermal conductivity

D_(T) is thermal diffusivity

Referring to FIG. 11, the effect of the prior pass may also beinfluenced by proximity of the instant energy beam location to an edgeor perimeter of the component being built. At an edge, there is lowerheat transport and heat thus accumulates to further increasetemperature. This effect is modeled and represented in the determinationof the temperature at the instant energy beam location as an edgefactor, f. The edge factor is a function of the distance from theinstant location of the energy beam to the edge.

${f(y)} = {1 + {\exp\left( {- \frac{{{Vl}_{tr}\left( {1 + {\cos\mspace{14mu}\beta}} \right)}y}{D_{T}L}} \right)}}$${{Imaginary}\mspace{14mu}{beam}\mspace{14mu}{with}\mspace{14mu}{effective}\mspace{14mu}{velocity}\mspace{14mu} v_{eff}} = {v_{l}\frac{l_{tr}}{L}}$Green  function  of  point  source ${\Delta\; T\begin{matrix}\rho \\(r) \\\;\end{matrix}} = {\frac{\alpha\; P}{2{\pi\kappa}\; r}{\exp\left( {- \frac{v_{eff}\left( {x + r} \right)}{2D_{T}}} \right)}\begin{matrix}{{r = {2\mspace{14mu} y}}\mspace{70mu}} \\{x = {2\mspace{14mu} y\mspace{14mu}\cos\mspace{14mu}\beta}}\end{matrix}}$ Referring  to  FIG.  12, Δ T₂  (previous  stripes):${\Delta\;{T_{2}\left( {x,y} \right)}} = {\frac{\alpha\; P}{4\pi\; L\;\kappa} \cdot {I\left( {x,y} \right)}}$${L_{r} = \frac{L}{\sqrt{4D_{T}\mspace{14mu} L\text{/}V}}},{V_{r} = \frac{l_{st}}{\sqrt{4D_{T}\mspace{14mu} L\text{/}V}}},{\left( {x,y} \right) = {{\left( {\frac{x^{\prime}}{L},\frac{y^{\prime}}{L}} \right)I} = {{\exp\left( {{- 2}V_{r}L_{r}x} \right)}\begin{Bmatrix}{{{2{{K_{0}\left( \left. {2 \cdot} \middle| {V_{r}L_{r}x} \right| \right)}\begin{bmatrix}{\left( {{{erf}\left( \frac{\left( {V_{r}L_{r}} \right)^{(0.5}\left( {0.5 + y} \right)}{|x|^{0.5}} \right)} + {{erf}\left( \frac{\left( {V_{r}L_{r}} \right)^{0.5}\left( {0.5 - y} \right)}{|x|^{0.5}} \right)}} \right) + {\frac{\left( {V_{r}L_{r}} \right)^{0.5}}{\left| {\pi\mspace{14mu} x} \right|^{0.5}} \cdot}} \\{\cdot \left( {{\left( {0.5 + y} \right){\exp\left( {- \frac{V_{r}{L_{r}\left( {0.5 + y} \right)}^{2}}{|x|}} \right)}} + {\left( {0.5 - y} \right){\exp\left( {- \frac{V_{r}{L_{r}\left( {0.5 - y} \right)}^{2}}{|x|}} \right)}}} \right)}\end{bmatrix}}} -}\mspace{95mu}} \\{{- \frac{\left( {V_{r}L_{r}} \right)^{0.5}}{\left| {\pi\mspace{14mu} x} \right|^{0.5}}} \cdot \left( {2{K_{1}\left( \left. {2 \cdot} \middle| {V_{r}L_{r}x} \right| \right)}} \right) \cdot \left( {{\left( {0.5 + y} \right){\exp\left( {- \frac{V_{r}{L_{r}\left( {0.5 + y} \right)}^{2}}{|x|}} \right)}} + {\left( {0.5 - y} \right){\exp\left( {- \frac{V_{r}{L_{r}\left( {0.5 - y} \right)}^{2}}{|x|}} \right)}}} \right)}\end{Bmatrix}}}}$ K₀(z)  and  K₁(z)  is  Bessel  functionsReferring  to  FIG.  13, Δ T₃  (previous  layers):${\Delta\; T_{3}} = {\frac{2P}{A\mspace{14mu}\kappa\; h}{\sum\limits_{k = 0}^{\infty}\;{\left\lbrack {\left( {- 1} \right)^{k} \cdot \frac{\sin\left( {\sqrt{\lambda_{k}}h} \right)}{\lambda_{k}}} \right\rbrack{\left( {{\exp\left( {{- D_{T}}\lambda_{k}\tau_{d}} \right)} - {\exp\left( {{- D_{T}}\lambda_{k}\tau_{p}} \right)}} \right) \cdot \left( \frac{1 - {\exp\left( {{- D_{T}}\lambda_{k}t} \right)}}{1 - {\exp\left( {{- D_{T}}\lambda_{k}\tau_{p}} \right)}} \right)}}}}$$\lambda_{k} = \left( \frac{\pi\left( {{2k} + 1} \right)}{2h} \right)^{2}$$\tau = \frac{A}{l_{st}V}$ τ_(p) = τ + τ_(d)

P is laser power

A is part surface area

h is the distance of part top surface from the build plate

τ is the time of one layer hatching

τ_(d) is delay time

n is the number of formed layers

Δh is layer thickness

Example 7: Model of Distribution of Temperature and Defects

As shown in the example of FIG. 14, a distribution of temperature can bemapped on the energy beam path. In this example, the path stripes areangled to the right in the figure. Each point in the map represents thetemperature, i.e., the temperature T₀ in the point (x,y) at a timemoment, when the energy beam passes that point.

As shown in FIG. 15, a distribution of defects can also be mapped. Inthis example, the distribution of defects is mapped in a layer locatedat height h from the build plate 22 a. As shown in FIG. 16, rather thana singular height, a distribution of defects can also be mapped in athree-dimensional volumetric space of the component. In this example,the distribution reveals a non-optimal build in which there arerepeating point defects and repeating linear defects.

Example 8: Model of Downskin

FIG. 17 shows a micrograph of a downskin perimeter region of a componentwith porosity defects. The occurrence of such defects is modeled andprovides opportunity to employ a control scheme to reduce occurrence ofsuch defects. A “downskin” is a section of a component that overhangsthe powder in the work bed 22 (versus a section that is on top of thecomponent).

FIG. 18 illustrates a representative model of a downskin section and thepath of the energy beam in a stripe at the edge. The downskinaccumulates heat because of low thermal conductivity of the powder. Theheat, in turn, causes defects such as porosity and excessive surfaceroughness. As shown in FIG. 19, the angle (φ) is the compliment to theangle (ψ) of the downskin section. The angle (φ) has a strong influenceon the accumulation of heat. Thus, for higher angles (φ), whichcorrespond to lower angles (ψ), there is greater heat accumulation andcorrespondingly higher temperature increase. This indicates that fordefects that occur due to excessive temperature in the downskin region,decreasing the angle (φ) will reduce temperature in the downskin region.

     Temperature  profile  in  downskin  region:${T(z)} = {T_{0} + {T_{ref}{\sum\limits_{n = 1}^{\infty}\;{\int\limits_{0}^{1}{\frac{d\;\xi}{\left( {{2n} - \xi} \right)^{3\text{/}2}}{\exp\left\lbrack {- \frac{\xi^{2} + \left( {\frac{{\left( {{2n} - 1} \right)l_{tr}} + z}{L} + {\xi\mspace{14mu}\tan\mspace{14mu}\alpha}} \right)^{2}}{4{B\left( {{2n} - \xi} \right)}}} \right\rbrack}}}}} + {T_{ref}{\sum\limits_{n = 1}^{\infty}\;{\int\limits_{0}^{1}{\frac{d\;\xi}{\left( {{2n} + \xi} \right)^{3\text{/}2}}{\exp\left\lbrack {- \frac{\xi^{2} + \left( {\frac{{2{nl}_{tr}} + z}{L} + {\xi\mspace{14mu}\tan\mspace{14mu}\alpha}} \right)^{2}}{4{B\left( {{2n} + \xi} \right)}}} \right\rbrack}}}}}}$$\mspace{76mu}{{T_{ref}\left( {P,v_{l},\varphi,\alpha} \right)} = {\frac{aP}{4{\varphi\kappa}}\sqrt{\frac{v_{l}\mspace{14mu}\cos\mspace{14mu}\alpha}{\pi\;{LD}_{T}}}}}$$\mspace{76mu}{B = \frac{D_{T}}{{Lv}_{l}\mspace{14mu}\cos\mspace{14mu}\alpha}}$     Equation  for  downskin  control:$\mspace{76mu}{{f(V)} = {\max_{m}\left( {\sum\limits_{n = 1}^{N}\;{\sqrt{\pi}{{\exp\left( \frac{n}{B} \right)}\left\lbrack {\frac{u_{n}(m)}{2a_{1}} + \frac{v_{n}(m)}{2a_{2}}} \right\rbrack}}} \right)}}$$\mspace{76mu}{{P\left( {V,\varphi} \right)} = {\left( {T_{melt} - T_{0}} \right)\frac{4\left( {{\pi\text{/}2} - \varphi} \right)\kappa}{\alpha_{abs}{f(V)}}\sqrt{\frac{\pi\;{LD}_{T}}{V}}}}$$\mspace{76mu}{{wherein},{{u_{n}(m)} = {\left\{ {{{- \frac{1}{\sqrt{\pi}}}\frac{e^{{- \frac{a_{1}^{2}}{{2n} - 1}} - {b^{2}{({{2n} - 1})}}}}{\frac{a_{1}}{\sqrt{{2n} - 1}}\left( {1 + \frac{\left( {{2n} - 1} \right)b}{a_{1}}} \right)}} + {e^{{- 2}a_{1}b}\left\lbrack {1 + {{erf}\left( {\frac{\alpha_{1^{\prime}}}{\sqrt{{2n} - 1}} - {b\sqrt{{2n} - 1}}} \right)}} \right\rbrack}} \right\} - \left\{ {{{- \frac{1}{\sqrt{\pi}}}\frac{e^{{- \frac{a_{1}^{2}}{2n}} - {2{nb}^{2}}}}{\frac{a_{1}}{\sqrt{2n}}\left( {1 + \frac{2{nb}}{a_{1}}} \right)}} + {e^{{- 2}a_{1}b}\left\lbrack {1 + {{erf}\left( {\frac{a_{1}}{\sqrt{2n}} - {b\sqrt{2n}}} \right)}} \right\rbrack}} \right\}}}}$${v_{n}(m)} = {\left\{ {{{- \frac{1}{\sqrt{\pi}}}\frac{e^{{- \frac{a_{2}^{2}}{2n}} - {2{nb}^{2}}}}{\frac{a_{2}}{\sqrt{2n}}\left( {1 + \frac{2{nb}}{a_{2}}} \right)}} + {e^{{- 2}a_{2}b}\left\lbrack {1 + {{erf}\left( {\frac{\alpha_{2}}{\sqrt{2n}} - {b\sqrt{2n}}} \right)}} \right\rbrack}} \right\} - \left\{ {{{- \frac{1}{\sqrt{\pi}}}\frac{e^{{- \frac{a_{2}^{2}}{{2n} + 1}} - {2{({n + 1})}b^{2}}}}{\frac{a_{2}}{\sqrt{{2n} + 1}}\left( {1 + \frac{\left( {{2n} + 1} \right)b}{a_{2}}} \right)}} + {e^{{- 2}a_{2}b}\left\lbrack {1 + {{erf}\left( {\frac{a_{2}}{\sqrt{{2n} + 1}} - {b\sqrt{{2n} + 1}}} \right)}} \right\rbrack}} \right\}}$$\mspace{76mu}{B = \frac{D_{T}}{LV}}$$\mspace{76mu}{l_{str} = \frac{l_{tr}}{L}}$$\mspace{76mu}{a_{1} = \sqrt{\frac{{4n^{2}} + {l_{str}^{2}\left( {{2n} + m - 1} \right)}^{2}}{4B}}}$$\mspace{76mu}{a_{2}\sqrt{\frac{{4n^{2}} + {l_{str}^{2}\left( {{2n} + m} \right)}^{2}}{4B}}}$$\mspace{76mu}{b = \sqrt{\frac{1}{4B}}}$

Although a combination of features is shown in the illustrated examples,not all of them need to be combined to realize the benefits of variousembodiments of this disclosure. In other words, a system designedaccording to an embodiment of this disclosure will not necessarilyinclude all of the features shown in any one of the Figures or all ofthe portions schematically shown in the Figures. Moreover, selectedfeatures of one example embodiment may be combined with selectedfeatures of other example embodiments.

The preceding description is exemplary rather than limiting in nature.Variations and modifications to the disclosed examples may becomeapparent to those skilled in the art that do not necessarily depart fromthis disclosure. The scope of legal protection given to this disclosurecan only be determined by studying the following claims.

What is claimed is:
 1. A powder processing machine comprising: a workbed; a powder deposition device operable to deposit powder in the workbed; at least one energy beam device operable to emit an energy beamwith a variable beam power and direct the energy beam onto the work bedwith a variable beam scan rate to melt and fuse regions of the powder;and a controller operable to dynamically control at least one of thebeam power or the beam scan rate to change how the powder melts andfuses, the controller configured to determine whether an instant set ofprocess parameters falls within a defect condition or a non-defectcondition and adjust at least one of the beam power or the beam scanrate responsive to the defect condition such that the instant set ofprocess parameters falls within the non-defect condition, the instantset of process parameters including an instant temperature at an instantlocation of the energy beam in the work bed, and the instant temperatureis based, at least in part, on an edge factor that represents an instantlocation of the energy beam in the work bed relative to an edge of acomponent being formed from the powder.
 2. The powder processing machineas recited in claim 1, wherein the instant temperature is determinedbased, at least in part, on a temperature of a build plate surface inthe work bed.
 3. The powder processing machine as recited in claim 1,wherein the instant temperature is based, at least in part, on atemperature change due to previous energy beam passes in a currentstripe.
 4. The powder processing machine as recited in claim 1, whereinthe instant temperature is based, at least in part, on a temperaturechange due to a previous stripe.
 5. The powder processing machine asrecited in claim 1, wherein the instant temperature is based, at leastin part, on a temperature change due to previous powder layers.
 6. Thepowder processing machine as recited in claim 1, wherein the instanttemperature is T₀=T_(BP)+ΔT₁f+ΔT₂+ΔT₃, where T₀ is the instanttemperature, T_(BP) is a temperature of a build plate surface in thework bed, ΔT₁ is a temperature change due to previous energy beam passesin a current stripe, ΔT₂ is a temperature change due to a previousstripe, ΔT₃ is a temperature change due to previous powder layers, and fis an edge factor that represents an instant location of the energy beamin the work bed relative to an edge of a component being formed from thepowder.
 7. The powder processing machine as recited in claim 1, whereinthe defect condition and non-defect condition are based, at least inpart, on at least one of an instant surface stress of a melt pool of thepowder at an instant location of the energy beam in the work bed, anenergy density of the energy beam and an instant cross-sectional area ofa melt pool of the powder at an instant location of the energy beam inthe work bed, or an instant diameter of a melt pool of the powder at aninstant location of the energy beam in the work bed.
 8. A powderprocessing machine comprising: a work bed; a powder deposition deviceoperable to deposit powder in the work bed; at least one energy beamdevice operable to emit an energy beam with a variable beam power anddirect the energy beam onto the work bed with a variable beam scan rateto melt and fuse regions of the powder; and a non-transitorycomputer-readable media comprising instructions, operable when executed,to: dynamically control at least one of the variable beam power or thevariable beam scan rate of the energy beam in the powder processingmachine to change how a powder melts and fuses in the work bed of thepowder processing machine, by determining whether an instant set ofprocess parameters falls within a defect condition or a non-defectcondition, and adjusting at least one of the variable beam power or thevariable beam scan rate responsive to the defect condition such that theinstant set of process parameters falls within the non-defect condition,the instant set of process parameters including an instant temperatureat an instant location of the energy beam in the work bed, and theinstant temperature is based, at least in part, on an edge factor thatrepresents an instant location of the energy beam in the work bedrelative to an edge of a component being formed from the powder.
 9. Thepowder processing machine as recited in claim 8, wherein the instanttemperature is determined based on at least one of a temperature of abuild plate surf ace in the work bed, a temperature change due toprevious energy beam passes in a current stripe, a temperature changedue to a previous stripe in the same layer, or a temperature change dueto previous powder layers.
 10. The powder processing machine as recitedin claim 8, wherein the instant temperature is T₀=T_(BP)+ΔT₁f+ΔT₂+ΔT₃,where T₀ is the instant temperature, T BP is a temperature of a buildplate surface in the work bed, ΔT₁ is a temperature change due toprevious energy beam passes in a current stripe, ΔT₂ is a temperaturechange due to a previous stripe in the same layer, ΔT₃ is a temperaturechange due to previous powder layers, and f is an edge factor thatrepresents an instant location of the energy beam in the work bedrelative to an edge of the component being formed from the powder. 11.The powder processing machine as recited in claim 8, wherein the defectcondition and non-defect condition are based, at least one part, on atleast one of an instant surface stress of a melt pool of the powder atan instant location of the energy beam in a work bed, an energy densityof the energy beam and an instant cross-sectional area of a melt pool ofthe powder at an instant location of the energy beam in the work bed, oran instant diameter of a melt pool of the powder at an instant locationof the energy beam in the work bed.
 12. The powder processing machine asrecited in claim 8, including adjusting the beam power by adjusting atime that the energy beam is on (non-zero power) and off (zero power).13. A method for use in a powder processing machine, the methodcomprising: dynamically controlling at least one of a beam power or abeam scan rate of an energy beam in a powder processing machine tochange how a powder melts and fuses in a work bed of the powderprocessing machine, by determining whether an instant set of processparameters falls within a defect condition or a non-defect condition,and adjusting at least one of the beam power or the beam scan rateresponsive to the defect condition such that the instant set of processparameters falls within the non-defect condition, the instant set ofprocess parameters including an instant temperature at an instantlocation of the energy beam in the work bed, and the instant temperatureis based, at least in part, on an edge factor that represents an instantlocation of the energy beam in the work bed relative to an edge of acomponent being formed from the powder.
 14. The method as recited inclaim 13, wherein the instant temperature is determined base, at leastin part, on at least one of a temperature of a build plate surface inthe work bed, a temperature change due to previous energy beam passes ina current stripe, a temperature change due to a previous stripe in thesame layer, or a temperature change due to previous powder layers. 15.The method as recited in claim 13, wherein the instant temperature isT₀=T_(BP)+ΔT₁f+ΔT₂+ΔT₃, where T₀ is the instant temperature, T_(BP) is atemperature of a build plate surface in the work bed, ΔT₁ is atemperature change due to previous energy beam passes in a currentstripe, ΔT₂ is a temperature change due to a previous stripe in the samelayer, ΔT₃ is a temperature change due to previous powder layers, and fis an edge factor that represents an instant location of the energy beamin the work bed relative to an edge of the component being formed fromthe powder.
 16. The method as recited in claim 13, wherein the defectcondition and non-defect condition are based on at least one of aninstant surface stress of a melt pool of the powder at an instantlocation of the energy beam in a work bed, an energy density of theenergy beam and an instant cross-sectional area of a melt pool of thepowder at an instant location of the energy beam in the work bed, or aninstant diameter of a melt pool of the powder at an instant location ofthe energy beam in the work bed.
 17. The method as recited in claim 13,including adjusting the beam power by adjusting a time that the energybeam is on (non-zero power) and off (zero power).
 18. A method for usewith a powder processing machine that is operable in an additivemanufacturing process to melt and fuse a powder in a work bed by atleast one energy beam emitted from at least one energy beam device alonga path to form a component, the method comprising: simulatingtemperature location-by-location along a perimeter of a component in anadditive manufacturing process based on an instant set of processparameters, a power of the energy beam, a speed of the energy beam, andthe path of the energy beam, wherein the instant set of processparameters include an instant temperature at an instant location of theenergy beam in the work bed, and the instant temperature is based, atleast in part, on an edge factor that represents an instant location ofthe energy beam in the work bed relative to an edge of a component beingformed from the powder; comparing the simulated temperature to acritical temperature criteria for formation of a defect to determinelocation-by-location along the path whether the simulated temperaturewill result in formation of the defect; if the simulated temperature isdetermined to result in formation of the defect, adjusting at least oneof the power of the energy beam, the speed of the energy beam, or thepath of the energy beam and repeating the simulating and comparing untilthe simulated temperature will not result in formation of the defect;and using the adjusted power of the energy beam, speed of the energybeam, or path of the energy beam in the additive manufacturing processto actually make the component.
 19. The method as recited in claim 18,wherein the simulating of the temperature includes geometric parametersrepresenting the geometry of the perimeter of the component.
 20. Themethod as recited in claim 18, wherein the set of process parametersincludes a stripe width of the path and an angle of the perimeter of thecomponent.